To improve the resilience of the uncoded strategy to the straggler effects, a coded strategy was developed in [1]}. The key idea is to introduce redundancy into the computation by using the coding theory. In particular, similar to the uncoded strategy, the coded strategy first partitions both vectors \(a\)  and \(x\)  into small sub-vectors of equal length \(s\) . The difference is that the sub-vector length \(s\)  can be any value larger than \(\sqrt{\frac{N_{1}N_{2}}{P}}\) , and the \(\frac{N_{1}}{s}\)  sub-vectors of \(a\)  are encoded into \(\frac{Ps}{N_{2}}\)  sub-vectors with each having a length of \(s\) , by using a (\(\frac{Ps}{N_{2}}\) , \(\frac{N_{1}}{s}\) ) MDS code. The following equation shows how a Vandermonde matrix, denoted as \(V \in \mathbb {R}^{\frac{N_{1}}{s} \times \frac{Ps}{N_{2}}}\) , can be used to encode the set of \(\frac{N_1}{s}\)  sub-vectors, \(\lbrace a_1,a_2,...,a_{\frac{N_1}{s}}\rbrace \) , into a larger set of \(\frac{Ps}{N_2}\)  sub-vectors, \(\lbrace \hat{a}_1,\hat{a}_2,...,\hat{a}_{\frac{Ps}{N_2}}\rbrace \) :
\(\begin{bmatrix}\hat{a}_{1} \\\hat{a}_{2} \\\vdots \\\hat{a}_{\frac{Ps}{N_{2}}}\end{bmatrix} &=V \begin{bmatrix}a_{1} \\a_{2} \\\vdots \\a_{\frac{N_{1}}{s}} \\\end{bmatrix} \nonumber \\&= \begin{bmatrix}1 & g_{1} & g_{1}^{2} & \dots & g_{1}^{\frac{N_{1}}{s} - 1} \\1 & g_{2} & g_{2}^{2} & \dots & g_{2}^{\frac{N_{1}}{s} - 1} \\\vdots & \vdots & \vdots & \ddots & \vdots \\1 & g_{\frac{Ps}{N_{2}}} & g_{\frac{Ps}{N_{2}}}^{2} & \dots & g_{\frac{Ps}{N_{2}}}^{\frac{N_{1}}{s} - 1}\end{bmatrix}\begin{bmatrix}a_{1} \\a_{2} \\\vdots \\a_{\frac{N_{1}}{s}}\end{bmatrix} \nonumber \) 
